Problem: Simplify the following expression and state the condition under which the simplification is valid: $k = \dfrac{p^2 + 4p - 32}{p^2 - 4p}$
First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 4p - 32}{p^2 - 4p} = \dfrac{(p + 8)(p - 4)}{(p)(p - 4)} $ Notice that the term $(p - 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p - 4)$ gives: $k = \dfrac{p + 8}{p}$ Since we divided by $(p - 4)$, $p \neq 4$. $k = \dfrac{p + 8}{p}; \space p \neq 4$